Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T14:26:50.558Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

Published online by Cambridge University Press:  26 August 2009

MIN-HSING CHANG ,
AN-CHENG RUO  and
FALIN CHEN
MIN-HSING CHANG
Affiliation:
Department of Mechanical Engineering, Tatung University, Taipei 104, Taiwan
AN-CHENG RUO
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
FALIN CHEN*
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
*
†Email address for correspondence: falin@iam.ntu.edu.tw
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of electrohydrodynamic flow between two horizontal plates with a vertical electrical conductivity gradient has been investigated in the presence of an imposed weak shear flow. The weak shear flow is driven by the horizontal pressure gradient, and the electrical conductivity gradient is generated by the concentration variation of the charge-carrying solute. An external electric field is applied across the fluid layer, and then the interaction between the unstable stratification of electrohydrodynamic flow and the shear arising from the plane Poiseuille flow is studied. A linear stability analysis has been implemented by considering both the longitudinal and transverse modes. Unlike the thermally stratified plane Poiseuille flow in which the longitudinal mode always dominates the onset of instability and is virtually unaffected by the superimposed shear flow, the instability of this mixed electrohydrodynamic–Poiseuille flow system is found to depend heavily on the shear flow, and the transverse mode may prevail over the longitudinal mode when the momentum of shear flow is sufficiently small. Particularly, an oscillatory longitudinal mode is found to exist, and it may become the critical mode when the conductivity gradient is small enough. The present results verify that an imposed weak shear flow may enhance the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 191 - 215
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baygents, J. C. & Baldessari, F. 1998 Electrohydrodynamic instability in a thin fluid layer with an electrical conductivity gradient. Phys. Fluids 10, 301–311.CrossRefGoogle Scholar
Carriere, P. & Monkewitz, P. A. 1999 Convective versus absolute instability in mixed Rayleigh–Bénard–Poiseuille convection. J. Fluid Mech. 384, 243–262.CrossRefGoogle Scholar
Chen, C. H., Lin, H., Lele, S. K. & Santiago, J. G. 2005 Convective and absolute electrokinetic instability with conductivity gradients. J. Fluid Mech. 524, 263–303.CrossRefGoogle Scholar
Clever, R. M. & Busse, F. H. 1992 Three-dimensional convection in a horizontal fluid layer subjected to a constant shear. J. Fluid Mech. 234, 511–527.CrossRefGoogle Scholar
Gage, K. S. & Reid, W. H. 1968 The stability of thermally stratified plane Poiseuille flow. J. Fluid Mech. 33, 21–32.CrossRefGoogle Scholar
Hoburg, J. F. 1977 Internal electrohydrodynamic instability of liquids with collinear field and conductivity gradients. J. Fluid Mech. 84, 291–303.CrossRefGoogle Scholar
Hoburg, J. F. & Melcher, J. R. 1976 Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients. J. Fluid Mech. 73, 333–351.CrossRefGoogle Scholar
Hoburg, J. F. & Melcher, J. R. 1977 Electrohydrodynamic mixing and instability induced by co-linear fields and conductivity gradients. Phys. Fluids 20, 903–911.CrossRefGoogle Scholar
Li, F., Ozen, O., Aubry, N., Papageorgiou, D. T. & Petropoulos, P. G. 2007 Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel. J. Fluid Mech. 583, 347–377.CrossRefGoogle Scholar
Lin, H., Storey, D. B., Oddy, M. H., Chen, C. H. & Santiago, J. G. 2004 Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 16, 1922–1935.CrossRefGoogle Scholar
Melcher, J. R. 1973 Electrohydrodynamics. In Proceedings of the IUTAM 13th International Congress of Theoretical and Applied Mechanics (ed. Becker, E. & Mikhailov, G. K.) pp. 240–263. Springer.CrossRefGoogle Scholar
Melcher, J. R. & Firebaugh, M. S. 1967 travelling-wave bulk electroconvection induced across a temperature gradient. Phys. Fluids 10, 1178–1185.CrossRefGoogle Scholar
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111–146.CrossRefGoogle Scholar
Michael, D. H. & O'nell, M. E. 1970 Electrohydrodynamic instability in plane layers of fluid. J. Fluid Mech. 41, 571–580.CrossRefGoogle Scholar
Mosher, R. A., Saville, D. A. & Thormann, W. 1992 The Dynamics of Electrophoresis. VCH.Google Scholar
Oddy, M. H. & Santiago, J. G. 2005 Multiple-species model for electrokinetic instability. Phys. Fluids 17, 064108.CrossRefGoogle Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381–411.CrossRefGoogle Scholar
Storey, B. D. 2005 Direct numerical simulation of electrohydrodynamic flow instabilities in microchannels. Physica D 211, 151–167.CrossRefGoogle Scholar
Storey, B. D., Tilley, B. S., Lin, H. & Santiago, J. G. 2005 Electrokinetic instabilities in thin microchannels. Phys. Fluids 17, 018103.CrossRefGoogle Scholar
Tardu, S. 2004 Interfacial electrokinetic effect on the microchannel flow linear stability. Trans. ASME J. Fluids Engng 126, 10–13.CrossRefGoogle Scholar
Taylor, G. I. & McEwan, A. D. 1965 The stability of a horizontal fluid interface in a vertical electric field. J. Fluid Mech. 22, 1–15.CrossRefGoogle Scholar
Thaokar, R. M. & Kumaran, V. 2005 Electrohydrodynamic instability of the interface between two fluids confined in a channel. Phys. Fluids 17, 084104.CrossRefGoogle Scholar
Thormann, W., Mosher, R. A. & Bier, M. 1986 Experimental and theoretical dynamics of isoelectric focusing. J. Chromatogr. 351, 17.CrossRefGoogle Scholar
Turnbull, R. J. & Melcher, J. R. 1969 Electrohydrodynamic Rayleigh–Taylor bulk instability. Phys. Fluids 12, 1160–1166.CrossRefGoogle Scholar